The finite-temperature chiral phase transition is investigated for three flavours of staggered quarks on a lattice of temporal extent N-tau = 4. In the simulation we use an improved fermion action which reduces rotational symmetry breaking of the quark propagator ( p4-action), include fat-links to improve the flavour symmetry and use the tree level improved (1,2) gluon action. We study the nature of the phase transition for quark masses of ma = 0.025, ma = 0.05 and ma = 0.1 on lattices with spatial sizes of 8(3) and 16(3).